Vehicles may be equipped with bumper assemblies and impact protection structures that elastically and plastically deform to absorb energy in the event of an impact. A number of standards and tests currently exist. Various organizations are introducing a number of pedestrian regulations and rating criteria for automotive vehicles. As one example, test methods have been developed to assess the protection of an adult pedestrian by simulating leg-impact conditions during a car-to-pedestrian impact. Such criteria can affect the rigidity or feel of the bumper assemblies. Accordingly, bumper assemblies are desired that allow for static subjective rigidity, particularly in the vertical direction, while maintaining pedestrian performance.